#include<bits/stdc++.h>
using namespace std;
#define LIFESUCKS ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define ll long long
#define pll pair<ll, ll>
#define mll map<ll, ll>
#define vll vector<ll>
#define pb push_back
#define fi first
#define se second
#define all(c) c.begin(),c.end()
#define debug cout<<"I Love You\n";
#define Bitc(x, j) ((x >> j) & 1)
#define fu(i,a,b) for ( ll i = a; i <= b; i++ )
#define fd(i,b,a) for ( ll i = b; i >= a; i-- )
const ll Mod = 1e9 + 7;
const ll inf = (1ll << 31);
const ll lnf = (1ll << 60);
template <class X, class Y>
bool minimize (X &x, const Y &y){
X eps = 1e-9;
if (x > y + eps) {x = y; return 1;}
return 0;
}
template <class X, class Y>
bool maximize (X &x, const Y &y){
X eps = 1e-9;
if (x + eps < y) {x = y; return 1;}
return 0;
}
#define mxn 20'007
ll n, k;
vector<pll> graph[mxn];
namespace Love1 {
bool check () {
return ( n <= 20 );
}
struct Edge {
ll d, u;
bool operator < ( const Edge& other ) const {
return other.d > d;
}
};
ll f[27];
void DreamyLove () {
ll sad = lnf;
ll gf;
fu ( msk, 1, (1 << n) - 1 ) {
if ( __builtin_popcount(msk) != k ) continue;
ll cr = -lnf;
priority_queue<Edge> Q;
fu ( i, 1, n ) f[i] = lnf;
fu ( i, 0, n - 1 ) if ( Bitc(msk, i)) Q.push({0, i + 1}), f[i + 1] = 0;
while ( !Q.empty()) {
ll u = Q.top().u, d = Q.top().d;
Q.pop();
if ( d > f[u] ) continue;
for ( pll& it: graph[u]){
ll v = it.fi, w = it.se;
if ( f[v] <= f[u] + w ) continue;
f[v] = f[u] + w;
Q.push({ f[v], v });
}
}
fu ( i, 1, n ) maximize(cr, f[i]);
if( minimize(sad, cr)) gf = msk;
}
cout << sad << '\n';
fu ( j, 0, n - 1 ) if ( Bitc( gf, j)) cout << j + 1 << ' ';
//
}
} // namespace Love1
namespace Love3 {
bool check () {
fu ( i, 1, n ) {
if ( (i == 1 || i == n) && ( graph[i].size() == 1 )) continue;
if ( graph[i].size() != 2 ) return 0;
}
return 1;
}
ll g[mxn], pref[mxn], suf[mxn];
void dfs ( ll u, ll p ) {
for ( pll& it: graph[u] ) {
ll v = it.fi, w = it.se;
if ( v == p ) continue;
pref[v] = pref[u] + w;
dfs ( v, u );
suf[u] = suf[v] + w;
}
}
void DreamyLove () {
ll sad = lnf, gf;
dfs(1, 0);
// fu ( i, 1, n ) cout << i << " " << pref[i] << ' ' << suf[i] << '\n';
fu ( i, 1, n ) if( minimize(sad, max(pref[i], suf[i]))) gf = i;
cout << sad << '\n' << gf;
//
}
} // namespace Love3
void lovesper(const ll TestCase){
cin >> n >> k;
fu ( i, 2, n ) {
ll u, v, w; cin >> u >> v >> w;
graph[u].pb({v, w});
graph[v].pb({u, w});
}
if ( Love1::check()) {
Love1::DreamyLove();
return;
}
if ( Love3::check()) {
Love3::DreamyLove();
return;
}
}
signed main(){
LIFESUCKS
#define name "lovesper"
// freopen(name".inp", "r", stdin);
// freopen(name".out", "w", stdout);
ll test=1;
// cin >> test;
for (int i = 1; i <= test; i++){
lovesper(i);
if ( i < test ) cout << '\n';
}
return 0;
}
